If ∫ g(x) dx from a to b = 4a+b, then ∫ (g(x)+7) dx from a to b = ?

Question

If ∫ g(x) dx from a to b = 4a+b, then ∫ (g(x)+7) dx from a to b = ? please explain

Arturo O. · Accepted Answer

Use the property that 
 
∫(g + f)dx = ∫gdx + ∫fdx
 
∫ab[g(x) + 7]dx = ∫abg(x)dx + ∫ab7dx = (4a + b) + 7(b - a) = -3a + 8b

Bobosharif S. · Answer

∫abg(x)dx=4a+b,, ∫ab(g(x)+7)dx=∫abg(x)dx+∫ab7dx=
=4a+b+7(b-a)=-3a+8b.

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